Basic properties
| Modulus: | \(847\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 847.z
\(\chi_{847}(8,\cdot)\) \(\chi_{847}(29,\cdot)\) \(\chi_{847}(50,\cdot)\) \(\chi_{847}(57,\cdot)\) \(\chi_{847}(85,\cdot)\) \(\chi_{847}(106,\cdot)\) \(\chi_{847}(127,\cdot)\) \(\chi_{847}(134,\cdot)\) \(\chi_{847}(162,\cdot)\) \(\chi_{847}(183,\cdot)\) \(\chi_{847}(204,\cdot)\) \(\chi_{847}(211,\cdot)\) \(\chi_{847}(260,\cdot)\) \(\chi_{847}(281,\cdot)\) \(\chi_{847}(288,\cdot)\) \(\chi_{847}(316,\cdot)\) \(\chi_{847}(337,\cdot)\) \(\chi_{847}(358,\cdot)\) \(\chi_{847}(365,\cdot)\) \(\chi_{847}(393,\cdot)\) \(\chi_{847}(414,\cdot)\) \(\chi_{847}(435,\cdot)\) \(\chi_{847}(442,\cdot)\) \(\chi_{847}(470,\cdot)\) \(\chi_{847}(491,\cdot)\) \(\chi_{847}(512,\cdot)\) \(\chi_{847}(519,\cdot)\) \(\chi_{847}(547,\cdot)\) \(\chi_{847}(568,\cdot)\) \(\chi_{847}(589,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,365)\) → \((1,e\left(\frac{81}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(519, a) \) | \(-1\) | \(1\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{41}{110}\right)\) |